Within the two-leg t-J ladder, the spin dynamics of the pressure-induced two-leg ladder cuprate superconductor Sr(14-x)Ca(x)Cu(24)O(41). is studied based on the kinetic energy driven superconducting mechanism. It is shown that in the pressure-induced superconducting state, the incommensurate spin correlation appears in the underpressure regime, while the commensurate spin fluctuation emerges in the optimal pressure and overpressure regimes. In particular, the spin-lattice relaxation time is dominated by a temperature linear dependence term at low temperature followed by a peak developed below the superconducting transition temperature, in qualitative agreement with the experimental observation on Sr(14-x)Ca(x)Cu(24)O(41)..
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